Anglican Bishop Victoria Matthews said a new cathedral with a different design would be built in its place.
Conservationists, however, have asked for the plan to be reconsidered.
The quake, which struck on 22 February, was New Zealand’s worst natural disaster in 80 years and left 185 people dead.
The cathedral, built in the late 19th Century, is a Christchurch landmark.
But the 6.3-magnitude earthquake, which leveled thousands of buildings in the city, badly damaged its structure and it was further weakened by numerous aftershocks.
Bishop Victoria Matthews said that no “bulldozers or wrecking balls” would be used, and that the cathedral would be deconstructed “with the utmost care and respect”.
“We acknowledge the high level of community interest and sense of ownership as the cathedral was both an iconic building and a place of regular worship by many,” she said in a statement.
“However, this is now a very dangerous building that needs to be made safe.”
The statement gave no timescale for the demolition and rebuilding. Efforts would be made to retrieved heritage items including stained glass windows and memorial stones, it said.
“We are now looking to the future and creating a beautiful, inspiring, safe new cathedral but we understand it will take some time for any of these decisions to be made,” the bishop said.
Christchurch Mayor Bob Parker said the decision to demolish the cathedral was “heartbreaking” and was “not an easy decision for many of us to accept”.
Conservationists, however, are asking the church to reconsider its decision. They say that officials should explore more options to try and keep much of the current structure, New Zealand media reports said.
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